I have a function as $$E=\int_\Omega -\log\big( p_i(x)\big) dx$$ where $p_i(x)$ is density distribution which estimated by Parzen window method. $p_i(x)=\frac{1}{\Omega_i} \int_{\Omega_i}K_\sigma\big(I(x)-I(y)\big) dy$, $K_\sigma=\frac{1}{\sqrt{2\pi}\sigma}\exp{\frac{-z^2}{2\sigma^2}}$, and $\sigma$ is scalar parameter. $I$ is an image $I(x):\Omega \to \mathbb{R}$, $i$ is given.
So, which ones is correct for left side: $E(\sigma),E(x),E(x,\sigma)$ or other form?